Watch Your Adjoints! Lack of Mesh Convergence in Inviscid Adjoint Solutions

It has been long known that 2D and 3D inviscid adjoint solutions are generically singular at sharp trailing edges. In this paper, a concurrent effect is described by which wall boundary values of 2...

[1]  Arthur Stück,et al.  An adjoint view on flux consistency and strong wall boundary conditions to the Navier-Stokes equations , 2015, J. Comput. Phys..

[2]  Dirk Ekelschot.  Mesh adaptation strategies for compressible flows using a high-order spectral/hp element discretisation , 2016 .

[3]  R. Dwight,et al.  Numerical sensitivity analysis for aerodynamic optimization: A survey of approaches , 2010 .

[4]  A. Jameson.  Optimum aerodynamic design using CFD and control theory , 1995 .

[5]  Michael B. Giles,et al.  Analytic adjoint solutions for the quasi-one-dimensional Euler equations , 2001, Journal of Fluid Mechanics.

[6]  Antony Jameson,et al.  Reduction of the Adjoint Gradient Formula for Aerodynamic Shape Optimization Problems , 2003 .

[7]  Antony Jameson,et al.  Aerodynamic design via control theory , 1988, J. Sci. Comput..

[8]  D. Venditti,et al.  Grid adaptation for functional outputs: application to two-dimensional inviscid flows , 2002 .

[9]  On the Properties of Solutions of the 2D Adjoint Euler Equations , 2018, Computational Methods in Applied Sciences.

[10]  Qiqi Wang,et al.  Interpretation of Adjoint Solutions for Turbomachinery Flows , 2012 .

[11]  Denis Sipp,et al.  Stability, Receptivity, and Sensitivity Analyses of Buffeting Transonic Flow over a Profile , 2015 .

[12]  J. Alonso,et al.  Unsteady Continuous Adjoint Approach for Aerodynamic Design on Dynamic Meshes , 2015 .

[13]  Michael B. Giles,et al.  Discrete Adjoint Approximations with Shocks , 2003 .

[14]  M. Giles,et al.  Algorithm Developments for Discrete Adjoint Methods , 2003 .

[15]  Dimitri J. Mavriplis,et al.  Adjoint-Based Sensitivity Formulation for Fully Coupled Unsteady Aeroelasticity Problems , 2009 .

[16]  Enrique Zuazua,et al.  Systematic Continuous Adjoint Approach to Viscous Aerodynamic Design on Unstructured Grids , 2007 .

[17]  On the adjoint solution of the quasi‐1D Euler equations: the effect of boundary conditions and the numerical flux function , 2005 .

[18]  J. Eric,et al.  Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations , 1998 .

[19]  W. K. Anderson,et al.  Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation , 1997 .

[20]  David L. Darmofal,et al.  Adaptive precision methodology for flow optimization via discretization and iteration error control , 2004 .

[21]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[22]  Carlos Lozano,et al.  Discrete surprises in the computation of sensitivities from boundary integrals in the continuous adjoint approach to inviscid aerodynamic shape optimization , 2012 .

[23]  Antony Jameson,et al.  Finite-Volume Solutions to the Euler Equations in Transonic Flow , 1983 .

[24]  Michael B. Giles,et al.  Improved- lift and drag estimates using adjoint Euler equations , 1999 .

[25]  Stefan Ulbrich,et al.  Convergence of Linearized and Adjoint Approximations for Discontinuous Solutions of Conservation Laws. Part 1: Linearized Approximations and Linearized Output Functionals , 2010, SIAM J. Numer. Anal..

[26]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[27]  Antony Jameson,et al.  Continuous Adjoint Method for Unstructured Grids , 2008 .

[28]  Enrique Zuazua,et al.  2-D Euler Shape Design on Nonregular Flows Using Adjoint Rankine-Hugoniot Relations , 2008 .

[29]  Earll M. Murman,et al.  Total pressure loss in vortical solutions of the conical Euler equations , 1985 .

[30]  M. Giles,et al.  Adjoint Error Correction for Integral Outputs , 2003 .

[31]  Jason E. Hicken,et al.  Dual consistency and functional accuracy: a finite-difference perspective , 2014, J. Comput. Phys..

[32]  Stefan Ulbrich,et al.  Convergence of Linearized and Adjoint Approximations for Discontinuous Solutions of Conservation Laws. Part 2: Adjoint Approximations and Extensions , 2010, SIAM J. Numer. Anal..

[33]  C. Lozano.  Adjoint Viscous Sensitivity Derivatives with a Reduced Gradient Formulation , 2012 .

[34]  Carlos Lozano,et al.  On mesh sensitivities and boundary formulas for discrete adjoint-based gradients in inviscid aerodynamic shape optimization , 2017, J. Comput. Phys..

[35]  J. Ponsin,et al.  Remarks on the numerical solution of the adjoint quasi‐one‐dimensional Euler equations , 2012 .

[36]  Carlos Lozano,et al.  Singular and Discontinuous Solutions of the Adjoint Euler Equations , 2018, AIAA Journal.

[37]  Antony Jameson,et al.  Optimum Shape Design for Unsteady Flows with Time-Accurate Continuous and Discrete Adjoint Methods , 2007 .

[38]  M. Giles,et al.  Adjoint equations in CFD: duality, boundary conditions and solution behaviour , 1997 .

[39]  J. Alonso,et al.  SU2: An Open-Source Suite for Multiphysics Simulation and Design , 2016 .

[40]  Frédéric Alauzet,et al.  Continuous and discrete adjoints to the Euler equations for fluids , 2011, ArXiv.

[41]  C. Lozano.  A note on the dual consistency of the discrete adjoint quasi-one-dimensional Euler equations with cell-centered and cell-vertex central discretizations , 2016 .